Making a curved area in an object plane
Select the edge loop.
Snap the cursor to it (Shift+S-->Cursor to Selected).
Select other loops up to the top of the mesh.
Set the pivot point to "3D Cursor"





Hit S,0 and hit Enter.




If you want to make the flattened surface look like a square plane you may add one, and join it with your mesh using Bridge Edge Loops option. Delete some edge loops X, add a plane and subdivide it (W-->Subdivide). Select the edge loops as pictured below (remember you have to have the equal number of verices in each separate meshes to make a bridge). Then press Space, type bridge and select Bridge Edge Loops option.